An M/PH/1 queue with workload-dependent processing speed and vacations

Yutaka Sakuma (Corresponding author), Onno Boxma, Tuan Phung-Duc

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Motivated by the trade-off issue between delay performance and energy consumption in modern computer and communication systems, we consider a single-server queue with phase-type service requirements and with the following two special features: Firstly, the service speed is a piecewise constant function of the workload. Secondly, the server switches off when the system becomes empty, only to be activated again when the workload reaches a certain threshold. For this system, we obtain the steady-state workload distribution and its moments of any order. We use this result to choose the activation threshold such that a certain cost function, involving processing costs, activation costs and mean workload, is minimized.

Originele taal-2Engels
Pagina's (van-tot)373-405
Aantal pagina's33
TijdschriftQueueing Systems
Nummer van het tijdschrift3-4
StatusGepubliceerd - 1 aug. 2021

Bibliografische nota

Funding Information:
The research of the first and third authors was supported in part by JSPS Kakenhi Grant Numbers JP18K11186 and JP18K18006, respectively. The research of the second author was funded by the NWO Gravitation Program NETWORKS, Grant Number 024.002.003.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Copyright 2021 Elsevier B.V., All rights reserved.


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